How to Manipulate Roots & Exponents

By Charlotte Johnson
NA/AbleStock.com/Getty Images

Manipulating roots and exponents is one of the basic components of algebra. You will have to learn how to perform operations with roots and exponents in high school and college algebra classes, as well as in career fields that rely heavily on math, such as engineering. In order to manipulate roots and exponents, refer to a set of algebraic rules.

Step 1

Realize that a number or variable to the first power remains the same. For example, a^1 = a.

Step 2

Add exponents that have the same base in a multiplication problem. For instance, y^3 x y^4 = y^3+4. Therefore the answer is y^7.

Step 3

Multiply multiple exponents belonging to one base. For example, x^(2)(3) = x^2x3, which equals x^6.

Step 4

Subtract exponents of like bases in division problems. For instance, a^5 / a^2 = a^5-2, which equals a^3.

Step 5

Realize that any number or variable raised to the zero power equals 1.

Step 6

Treat negative exponents in a reciprocal fashion. For instance, x^-3 = 1/x^3.

Step 7

Divide exponents when a root sign is involved. For instance if there is a 2 exponent on the left side of the square root sign and an x^3 under the square root sign, the answer would be x^3/2.

Step 8

Realize that the square root of two multiplied variables equals the product of each variable squared. For example, the square root of xy equals the square root of x times the square root of y.

Step 9

Realize that the quotient of two variables under a square root sign equals the square root of the top variable divided by the square root of the bottom variable. For instance, the square root of x/y equals the square root of x divided by the square root of y.